The $n^{-2}$-Order Mean Squared Errors of the Maximum Likelihood and the Minimum Logit Chi-Square Estimator

Abstract

The $n^{-2}$ order mean squared errors of the maximum likelihood and the minimum chi-square estimator of the logit regression model are derived and the latter is shown to be superior for many parameter values considered. The maximum likelihood is shown to be better if the bias of each estimator is corrected to the order of $n^{-1}$; however, the difference is shown to be negligibly small in many practical situations.